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Abstract:

An electronic system is provided that simulates a glucose-insulin
metabolic system of a T2DM or prediabetic subject, wherein the system
includes a subsystem that models dynamic glucose concentration in a T2DM
or prediabetic subject, including an electronic module that models
endogenous glucose production (EGP(t)), or meal glucose rate of
appearance (Ra(t>>, or glucose utilization (U(t)), or renal
excretion of glucose (B(t)), a subsystem that models dynamic insulin
concentration in said T2DM or prediabetic subject, including an
electronic module that models insulin secretion (S(t)), an electronic
database containing a population of virtual T2DM or prediabetic subjects,
each virtual subject having a plurality of metabolic parameters, and a
processing module that calculates an effect of variation of at least one
metabolic parameter value on the glucose insulin metabolic system of a
virtual subject by inputting the plurality of metabolic parameter values.

Claims:

1. An electronic system that simulates a glucose-insulin metabolic system
of a T2DM or prediabetic subject, comprising: a subsystem that models
dynamic glucose concentration in a T2DM or prediabetic subject, including
an electronic module that models endogenous glucose production (EGP(t)),
an electronic module that models meal glucose rate of appearance (Ra(t)),
an electronic module that models glucose utilization (U(t)), an
electronic module that models renal excretion of glucose (E(t)); a
subsystem that models dynamic insulin concentration in said T2DM or
prediabetic subject, including an electronic module that models insulin
secretion (S(t)); an electronic database containing a population of
virtual T2DM or prediabetic subjects, each virtual subject having a
plurality of metabolic parameters with values within a range of values
derived from in vivo T2DM or prediabetic subjects; and a processing
module that calculates an effect of variation of at least one metabolic
parameter value on the glucose-insulin metabolic system of a virtual
subject by inputting said plurality of metabolic parameter values
including said at least one varied metabolic parameter value into said
glucose concentration and insulin concentration subsystems.

13. An electronic system as set forth in claim 1, wherein a prediabetic
subject is a subject with impaired fasting glucose (IFG).

14. An electronic system as set forth in claim 1, wherein a prediabetic
subject is a subject with impaired glucose tolerance (IGT).

15. An electronic system as set forth in claim 1, wherein said plurality
of metabolic parameters for each virtual subject includes at least one of
the following parameters: kabs=rate constant of glucose absorption
by the intestine kmax=maximum rate constant of gastric emptying
kmin=minimum rate constant of gastric emptying b=percentage of the
dose for which kempt decreases at (kmax-kmin)/2
c=percentage of the dose for which kempt is back to
(kmax-kmin)/2 ki=rate parameter accounting for delay
between insulin signal and insulin action on the liver kp2=liver
glucose effectiveness kp3=parameter governing amplitude of insulin
action on the liver kp4=parameter governing amplitude of portal
insulin action on the liver Vg=distribution volume of glucose
Vmx=parameter governing amplitude of insulin action on glucose
utilization km0=parameter governing glucose control on glucose
utilization K2=rate parameter accounting for glucose transit from
tissue to plasma K1=rate parameter accounting for glucose transit
from plasma to tissue p2U=rate parameter accounting for delay
between insulin signal and insulin action on glucose utilization
Vi=distribution volume of insulin K=beta-cell responsivity to
glucose rate of change β=beta-cell responsivity to glucose level
α=rate parameter accounting for delay between glucose signal and
insulin secretion m1=rate parameter of insulin kinetics
m5=coefficient linking insulin hepatic extraction to insulin
secretion rate Gb=basal plasma glucose concentration EGPb=basal
endogenous glucose production BW=body weight Ib=basal plasma insulin
concentration SRb=basal insulin secretion rate.

16. An electronic system as set forth in claim 1, wherein said subsystems
and modules are implemented as computer executable software stored on a
computer-readable storage medium and loaded into an electronic
programmable computer.

17. An electronic system as set forth in claim 1, wherein said subsystems
and modules are implemented as application specific integrated circuit
modules.

18. A computer-executable program product embodied as computer executable
code in a computer-readable storage medium, wherein said
computer-executable program product simulates a glucose-insulin metabolic
system of a T2DM or prediabetic subject, said computer-executable code
comprising: subsystem code that models dynamic glucose concentration in a
T2DM or prediabetic subject, including an electronic code module that
models endogenous glucose production (EGP(t)), an electronic code module
that models meal glucose rate of appearance (Ra(t)), an electronic code
module that models glucose utilization (U(t)), an electronic code module
that models renal excretion of glucose (E(t)); subsystem code that models
dynamic insulin concentration in said T2DM or prediabetic subject,
including an electronic code module that models insulin secretion (S(t));
an electronic database containing a population of virtual T2DM or
prediabetic subjects, each virtual subject having a plurality of
metabolic parameters with values within a range of values derived from in
vivo T2DM or prediabetic subjects; and computer-executable code that
calculates an effect of variation of at least one metabolic parameter
value on the glucose-insulin metabolic system of a virtual subject by
inputting said plurality of metabolic parameter values including said at
least one varied metabolic parameter value into said glucose
concentration and insulin concentration subsystems.

30. A computer-executable program product as set forth in claim 18,
wherein a prediabetic subject is a subject with impaired fasting glucose
(IFG).

31. A computer-executable program product as set forth in claim 18,
wherein a prediabetic subject is a subject with impaired glucose
tolerance (IGT).

32. A computer-executable program product as set forth in claim 18,
wherein said plurality of metabolic parameters for each virtual subject
includes at least one of the following parameters: kabs=rate
constant of glucose absorption by the intestine kmax=maximum rate
constant of gastric emptying kmin=minimum rate constant of gastric
emptying b=percentage of the dose for which kempt decreases at
(kmax-kmin)/2 c=percentage of the dose for which kempt is
back to (kmax-kmin)/2 ki=rate parameter accounting for
delay between insulin signal and insulin action on the liver
kp2=liver glucose effectiveness kp3=parameter governing
amplitude of insulin action on the liver kp4=parameter governing
amplitude of portal insulin action on the liver Vg=distribution
volume of glucose Vmx=parameter governing amplitude of insulin
action on glucose utilization km0=parameter governing glucose
control on glucose utilization K2=rate parameter accounting for
glucose transit from tissue to plasma K1=rate parameter accounting
for glucose transit from plasma to tissue p2U=rate parameter
accounting for delay between insulin signal and insulin action on glucose
utilization Vi=distribution volume of insulin K=beta-cell
responsivity to glucose rate of change β=beta-cell responsivity to
glucose level α=rate parameter accounting for delay between glucose
signal and insulin secretion m1=rate parameter of insulin kinetics
m5=coefficient linking insulin hepatic extraction to insulin
secretion rate Gb=basal plasma glucose concentration EGPb=basal
endogenous glucose production BW=body weight Ib=basal plasma insulin
concentration SRb=basal insulin secretion rate.

Description:

BACKGROUND OF THE INVENTION

[0001] Over 20 million people in the United States alone have Type 2
Diabetes Mellitus (T2DM)--a complex derangement of the glucose-insulin
metabolic system, which results in an increased insulin resistance and
inappropriate insulin secretion. However, this pathological state does
not appear suddenly, but usually subjects move from a healthy state to a
diabetic state passing through an intermediate phase, called prediabetes:
e.g. it is well known that individuals with impaired fasting glucose
(IFG) have a 20-30% chance of developing diabetes over the following 5-10
years [1-3]. The risk is even greater if they have combined IFG and
impaired glucose tolerance (IGT). Furthermore, IFG and IGT are associated
with increased risk of cardiovascular events [4, 5]. Therefore, in
addition to studies on T2DM, the pathogenesis of IFG alone or in
combination with IGT has engendered considerable interest. For instance,
recently, it has been shown that postprandial hyperglycemia in
individuals with early diabetes is due to lower rates of glucose
disappearance rather than increased meal appearance or impaired
suppression of endogenous glucose production (EGP), regardless of their
fasting glucose. In contrast, insulin secretion, action, and the pattern
of postprandial turnover are essentially normal in individuals with
isolated IFG [6]. These results suggest that for treatment and prevention
of T2DM it is very important to provide drugs with a specific target,
e.g. the ability to stimulate secretion instead of increasing insulin
secretion, if this is the case.

[0002] To this purpose it is essential to investigate the mechanisms of
glucose-inulin system derangement and drug pharmacodynamics, with
properly designed experimental trials. However, it may not be possible,
appropriate, convenient or desirable to perform such evaluation
experiments on the diabetic subject in vivo, because some experiments
cannot be done at all, or are too difficult, too dangerous, too expensive
or not ethical. An in silica simulation environment could offer an
alternative tool to test different treatment strategies, e.g. drug,
exercise, diet, in prediabetes and diabetes in a cost-effective way. The
power of simulation tools has been recently recognized by the FDA (Food
and Drug Administration) which accepted a simulator of Type 1 Diabetes
(T1DM) [7, 8] as an alternative to the animal studies for the validation
of control algorithms before their use in human clinical trials [9]. No
such simulator of T2DM has existed heretofore.

SUMMARY OF THE INVENTION

[0003] An aspect of an embodiment of the present invention extends the
simulation of T1DM to T2DM. It is important to emphasize that due to the
profound physiological differences between T1DM and T2DM, the
mathematical model and the simulated "subjects" with T2DM are very
different from the model and simulated "population" of T1DM.

[0004] Realistic computer simulation can provide invaluable information
about the safety and the limitations of various treatments of T2DM, can
guide and focus the emphasis of clinical studies, and can rule-out
ineffective treatment scenarios in a cost-effective manner prior to human
use. While simulators of diabetes exist, most are based on general
population models. As a result, their capabilities are generally limited
to prediction of population averages that would be observed during
clinical trials.

[0005] Therefore, for the purpose of personalized treatment development, a
different type of computer simulator is needed--a system that is capable
of simulating the glucose-insulin dynamics of a particular person. In
other words, a simulator of T2DM should be equipped with a "cohort" of in
silico "subjects" that spans sufficiently well the observed inter-person
variability of key metabolic parameters in the general population of
people with T2DM. Because large-scale simulations would account better
for inter-subject variability than small-size animal trials and would
allow for more extensive testing of the limits and robustness of various
treatments, the following paradigm has emerged: (i) in silico modeling
could produce credible pre-clinical results that could be substituted for
certain animal trials, and (ii) in silico testing yields these results in
a fraction of the time required for animal trials.

[0006] Following this paradigm, this invention provides a comprehensive
simulation environment, which has the potential to accelerate studies on
T2DM and prediabetes. Two exemplary principal components of the
simulation environment are: (1) A mathematical model of the human
metabolic system which has been derived from a unique data set, including
both T2DM and prediabetic patients who underwent a triple tracer meal
protocol, and (2) A population of virtual subjects including N=100
subjects with pre-diabetes and N=100 subjects with T2DM. As previously
demonstrated by our simulator of Type 1 Diabetes, a comprehensive
simulation environment has the potential for performing rapid and
cost-effective in silica experiments. T2DM specific experiments on
virtual subjects could test the efficacy of drugs and other treatments,
e.g. exercise or diet, for improving prediabetes and T2DM control.

[0007] In accordance with a first aspect of the invention, an electronic
system is provided that simulates a glucose-insulin metabolic system of a
T2DM or prediabetic subject, wherein the system includes a subsystem that
models dynamic glucose concentration in a T2DM or prediabetic subject,
including [0008] an electronic module that models endogenous glucose
production (EGP(t), [0009] an electronic module that models meal glucose
rate of appearance (Ra(t)), [0010] an electronic module that models
glucose utilization (U(t)), [0011] an electronic module that models renal
excretion of glucose (E(t));

[0012] a subsystem that models dynamic insulin concentration in said T2DM
or prediabetic subject, including [0013] an electronic module that
models insulin secretion (S(t));

[0014] an electronic database containing a population of virtual T2DM or
prediabetic subjects, each virtual subject having a plurality of
metabolic parameters with values within a range of values derived from in
vivo T2DM or prediabetic subjects; and

[0015] a processing module that calculates an effect of variation of at
least one metabolic parameter value on the glucose-insulin metabolic
system of a virtual subject by inputting said plurality of metabolic
parameter values including said at least one varied metabolic parameter
value into said glucose concentration and insulin concentration
subsystems.

[0016] In accordance with a second aspect of the invention, a
computer-executable program product embodied as computer executable code
in a computer-readable storage medium is provided, wherein said
computer-executable program product simulates a glucose-insulin metabolic
system of a T2DM or prediabetic subject, said computer-executable code
including subsystem code that models dynamic glucose concentration in a
T2DM or prediabetic subject, including [0017] an electronic code module
that models endogenous glucose production (EGP(t)), [0018] an electronic
code module that models meal glucose rate of appearance (Ra(t)), [0019]
an electronic code module that models glucose utilization (U(t)), [0020]
an electronic code module that models renal excretion of glucose (E(t));

[0023] an electronic database containing a population of virtual T2DM or
prediabetic subjects, each virtual subject having a plurality of
metabolic parameters with values within a range of values derived from in
vivo T2DM or prediabetic subjects; and

[0024] computer-executable code that calculates an effect of variation of
at least one metabolic parameter value on the glucose-insulin metabolic
system of a virtual subject by inputting said plurality of metabolic
parameter values including said at least one varied metabolic parameter
value into said glucose concentration and insulin concentration
subsystems.

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1 is a set of graphs illustrating plasma glucose and insulin
concentrations, meal rate of appearance and endogenous glucose
production, and glucose utilization and insulin secretion rate;

[0029]FIG. 5 is a schematic block diagram for a system or related method
of an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0030] Two key components of the simulator of the glucose-insulin
metabolic system in prediabetes and T2DM in accordance with the present
invention are:

[0031] (1) A physiological model of glucose-insulin metabolism in
prediabetes and T2DM, and

[0032] (2) A population of virtual subjects with prediabetes (N=100) and
T2DM (N=100).

Physiological Model of Glucose-Insulin Metabolism in Prediabetes and T2DM

[0033] Both model equations and the procedures which were used to identify
model parameter distributions from prediabetes and T2DM meal data and to
generate the virtual subject population are now described in accordance
with an embodiment of the invention.

where Ip and II (pmol/kg) are insulin masses in plasma and in
the liver, respectively; I (pmol/l) is plasma insulin concentration; S is
insulin secretion (pmol/kg/min); VI is the distribution volume of
insulin (l/kg); and m1-m4 (min-1) are rate parameters.

[0040] Degradation, D, occurs both in the liver and peripherally.
Peripheral degradation has been assumed to be linear (m4). Hepatic
extraction of insulin, HE, i.e. the insulin flux which leaves the liver
irreversibly, divided by the total insulin flux leaving the liver, is
assumed to be dependent from insulin secretion, S:

kp1 (mg/kg/min) is the extrapolated EGP at zero glucose and insulin;
kp2 (min-1) is liver glucose effectiveness; kp3 (mg/kg/min
per pmol/l) is a parameter governing amplitude of insulin action on the
liver; kp4 (mg/kg/min/(pmol/kg)) is a parameter governing amplitude
of portal insulin action on the liver; and ki (min-1) is a rate
parameter accounting for the delay between an insulin signal and insulin
action. EGP is obviously constrained to be non-negative. At basal steady
state one has:

kp1=EGPb+kp2Gpb+kp3Ib+kp4Ipob
(12)

Glucose Rate of Appearance

[0042] The glucose rate of appearance (Ra) is defined by the following
group of equations (13):

where Qsto (mg) is the amount of glucose in the stomach (solid
phase, Qsto1, and liquid phase, Qsto2); Qgut (mg) is the
glucose mass in the intestine; kgri(min-1) is the rate of
grinding; kempt(Qsto) (min-1) is a rate constant of
gastric emptying which is a nonlinear function of Qsto; kabs
(min-1) is a rate constant of intestinal absorption; f is a fraction
of intestinal absorption which actually appears in the plasma; D (mg) is
an amount of ingested glucose; BW (kg) is body weight; and Ra (mg/kg/min)
is the appearance rate of glucose in the plasma.

Glucose Utilization

[0043] Glucose utilization is made up of two components:
insulin-independent utilization and insulin-dependent utilization.
Insulin-independent utilization takes place in the first compartment, is
constant and represents glucose uptake by the brain and erythrocytes
(Fcns):

Uii(t)=Fcns (14)

Insulin-dependent utilization takes place in the remote compartment and
depends nonlinearly (Michaelis Menten) from glucose in the tissues:

where γ (min-1) is the transfer rate constant between the
portal vein and the liver; K (pmol/kg per mg/dl) is the pancreatic
responsivity to glucose rate of change; a (min-1) is the delay
between the glucose signal and insulin secretion; β (pmol/kg/min per
mg/dl) is the pancreatic responsivity to the glucose level; and h (mg/dl)
is the threshold level of glucose above which the β-cells initiate
to produce new insulin (h was set to the basal glucose concentration
Gb to guarantee system steady state in basal condition).

Renal Glucose Excretion

[0045] Renal glucose excretion, E, is defined by the following equation
(25):

where ke1(min-1) is the glomerular filtration rate; and
ke2(mg/kg) is the renal threshold of glucose.

[0046] b. Parameter Identification

[0047] The data base used to identify the model consisted of 35 subjects
with either IFG or IGT, or both (prediabetes), and 23 T2DM patients who
underwent a triple tracer meal protocol, thus allowing us to obtain in a
virtually model-independent fashion the time course of all of the
relevant glucose and insulin fluxes during a meal [6, 11]. Subject
characteristics are reported in Table 1. Average plasma glucose and
insulin concentration, Ra, EGP, U and SR in prediabetes and T2DM are
shown in FIG. 1 together with the profile obtained in a matched healthy
population [6]. In FIG. 1, plasma glucose and insulin concentrations are
shown in the upper panels, meal glucose rate of appearance and endogenous
glucose production are shown in the middle panels, and glucose
utilization and insulin secretion rate are shown in the lower panels, in
prediabetes, T2DM, and matched healthy subjects respectively.

[0048] The system model described in section (a) has been identified in
each subject by using a subsystem decomposition and forcing function
strategy, as shown in FIG. 2. In FIG. 2, a unit process model for
endogenous glucose production is shown in the top left panel; unit
process model for glucose rate of appearance is shown in the top right
panel; unit process model for glucose utilization is shown in the bottom
left panel; an unit process model for insulin secretion is shown in the
bottom right panel.

[0050] Model parameters were thus identified in each subject and
log-transformed. The average parameter vector and the covariance matrix
have been thus calculated for both prediabetic and T2DM populations.
Assuming that the parameter vector is a log-normally distributed random
vector, the average of log-transformed parameters and the covariance
matrix univocally define the joint parameter distribution. In order to
prove that the generated populations reflect the observed variability,
the range of simulated plasma glucose concentrations in both populations
(prediabetes and T2DM) is shown in FIG. 3, superimposed with the observed
(measured) range of variability.

[0051] A potential application of the simulator is the in silico study of
the effect of a drug on glucose metabolism. FIG. 4 shows plasma glucose
and insulin concentrations in untreated prediabetics versus a profile
obtained with the administration of a drug x, which increases insulin
sensitivity, and a drug y, which enhance beta-cell responsivity to
glucose.

Population of Virtual "Subjects" with Prediabetes (N=100) and T2DM
(N=100).

[0052] As noted above, the key to successful simulation is the
availability of a comprehensive population of simulated "subjects" that
encompasses the distribution of key metabolic parameters observed in T2DM
in vivo. From the joint parameter distributions described in the previous
section we have generated N=200 virtual subjects: N=100 with prediabetes
and N=100 with T2DM.

[0053] Each virtual subject is uniquely identified by a set of 26
parameters:

[0054] kabs=rate constant of glucose absorption by the intestine

[0055] kmax=maximum rate constant of gastric emptying

[0056] kmin=minimum rate constant of gastric emptying

[0057] b=percentage of the dose for which kempt decreases at
(kmax-kmin)/2

[0058] c=percentage of the dose for which kempt is back to
(kmax-kmin)/2

[0059] ki=rate parameter accounting for delay between insulin signal
and insulin action on the liver

[0060] kp2=liver glucose effectiveness

[0061] kp3=parameter governing amplitude of insulin action on the
liver

[0082]FIG. 5 is a functional block diagram for a computer system 500 for
implementation of an exemplary embodiment or portion of an embodiment of
the present invention. For example, a method or system of an embodiment
of the present invention may be implemented using hardware, software or a
combination thereof and may be implemented in one or more computer
systems or other processing systems, such as personal digit assistants
(PDAs) equipped with adequate memory and processing capabilities. In an
example embodiment, the invention was implemented in software running on
a general purpose computer 50 as illustrated in FIG. 5. The computer
system 500 may includes one or more processors, such as processor 504.
The Processor 504 is connected to a communication infrastructure 506
(e.g., a communications bus, cross-over bar, or network). The computer
system 500 may include a display interface 502 that forwards graphics,
text, and/or other data from the communication infrastructure 506 (or
from a frame buffer not shown) for display on the display unit 530.
Display unit 530 may be digital and/or analog.

[0083] The computer system 500 may also include a main memory 508,
preferably random access memory (RAM), and may also include a secondary
memory 510. The secondary memory 510 may include, for example, a hard
disk drive 512 and/or a removable storage drive 514, representing a
floppy disk drive, a magnetic tape drive, an optical disk drive, a flash
memory, etc. The removable storage drive 514 reads from and/or writes to
a removable storage unit 518 in a well known manner. Removable storage
unit 518, represents a floppy disk, magnetic tape, optical disk, etc.
which is read by and written to by removable storage drive 514. As will
be appreciated, the removable storage unit 518 includes a computer usable
storage medium having stored therein computer software and/or data.

[0084] In alternative embodiments, secondary memory 510 may include other
means for allowing computer programs or other instructions to be loaded
into computer system 500. Such means may include, for example, a
removable storage unit 522 and an interface 520. Examples of such
removable storage units/interfaces include a program cartridge and
cartridge interface (such as that found in video game devices), a
removable memory chip (such as a ROM, PROM, EPROM or EEPROM) and
associated socket, and other removable storage units 522 and interfaces
520 which allow software and data to be transferred from the removable
storage unit 522 to computer system 500.

[0085] The computer system 500 may also include a communications interface
524. Communications interface 124 allows software and data to be
transferred between computer system 500 and external devices. Examples of
communications interface 524 may include a modem, a network interface
(such as an Ethernet card), a communications port (e.g., serial or
parallel, etc.), a PCMCIA slot and card, a modem, etc. Software and data
transferred via communications interface 524 are in the form of signals
528 which may be electronic, electromagnetic, optical or other signals
capable of being received by communications interface 524. Signals 528
are provided to communications interface 524 via a communications path
(i.e., channel) 526. Channel 526 (or any other communication means or
channel disclosed herein) carries signals 528 and may be implemented
using wire or cable, fiber optics, blue tooth, a phone line, a cellular
phone link, an RF link, an infrared link, wireless link or connection and
other communications channels.

[0086] In this document, the terms "computer program medium" and "computer
usable medium" are used to generally refer to media or medium such as
various software, firmware, disks, drives, removable storage drive 514, a
hard disk installed in hard disk drive 512, and signals 528. These
computer program products ("computer program medium" and "computer usable
medium") are means for providing software to computer system 500. The
computer program product may comprise a computer useable medium having
computer program logic thereon. The invention includes such computer
program products. The "computer program product" and "computer useable
medium" may be any computer readable medium having computer logic
thereon.

[0087] Computer programs (also called computer control logic or computer
program logic) are may be stored in main memory 508 and/or secondary
memory 510. Computer programs may also be received via communications
interface 524. Such computer programs, when executed, enable computer
system 500 to perform the features of the present invention as discussed
herein. In particular, the computer programs, when executed, enable
processor 504 to perform the functions of the present invention.
Accordingly, such computer programs represent controllers of computer
system 500.

[0088] In an embodiment where the invention is implemented using software,
the software may be stored in a computer program product and loaded into
computer system 500 using removable storage drive 514, hard drive 512 or
communications interface 524. The control logic (software or computer
program logic), when executed by the processor 504, causes the processor
504 to perform the functions of the invention as described herein.

[0089] In another embodiment, the invention is implemented primarily in
hardware using, for example, hardware components such as application
specific integrated circuits (ASICs). Implementation of the hardware
state machine to perform the functions described herein will be apparent
to persons skilled in the relevant art(s).

[0090] In yet another embodiment, the invention is implemented using a
combination of both hardware and software.

[0091] In an example software embodiment of the invention, the methods
described above may be implemented in SPSS control language or C++
programming language, but could be implemented in other various programs,
computer simulation and computer-aided design, computer simulation
environment, MATLAB, or any other software platform or program, windows
interface or operating system (or other operating system) or other
programs known or available to those skilled in the art.

PUBLICATIONS

[0092] The following patents, applications and publications as listed
below and throughout this document are hereby incorporated by reference
in their entirety herein.